Details

sample24.0ms

Algorithm

intervals

Results

4.0ms	52×	body	1280	valid
4.0ms	229×	body	80	nan
3.0ms	46×	body	640	valid
3.0ms	135×	body	80	valid
1.0ms	17×	body	320	valid
0.0ms	6×	body	160	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.2b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

1.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

57×	`sqrt-prod`
50×	`*-un-lft-identity`
42×	`prod-diff`
37×	`add-sqr-sqrt`
29×	`add-cube-cbrt`
8×	`distribute-lft-out`
7×	`fma-neg`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `log1p-expm1-u`

Counts

1 → 70

Calls

1 calls:

11.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series74.0ms

Counts

1 → 3

Calls

1 calls:

74.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify137.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (122.0ms)

Iter	Nodes	Cost
0	249	1065
1	728	733
2	4106	623
3	5001	592

prune80.0ms

Filtered

73 candidates to 27 candidates (63.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	2	74

Merged error: 0.1b

Counts

74 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
32×	`distribute-lft-out`
28×	`sqrt-prod`
24×	`times-frac`
16×	`add-sqr-sqrt` `add-cube-cbrt`
7×	`fma-def`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 75

Calls

2 calls:

9.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
14.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series229.0ms

Counts

2 → 6

Calls

2 calls:

74.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
155.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	353	693
1	1416	627
2	5001	586

prune142.0ms

Filtered

81 candidates to 51 candidates (37.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	76	7	83

Merged error: 0.0b

Counts

83 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite165.0ms

Algorithm

rewrite-expression-head

Rules

960×	`*-un-lft-identity`
552×	`sqrt-prod`
495×	`sqrt-div`
421×	`distribute-lft-out`
247×	`times-frac`
225×	`frac-times`
210×	`associate-/r*`
196×	`add-sqr-sqrt`
165×	`add-cube-cbrt`
140×	`associate-/l*`
71×	`swap-sqr`
70×	`associate-/l/`
42×	`flip3-+` `flip-+`
35×	`frac-2neg` `clear-num`
33×	`associate-r` `associate-l`
20×	`pow1`
15×	`associate-r/` `associate-l/`
14×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`div-inv`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `div-exp`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 590

Calls

4 calls:

19.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
61.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series877.0ms

Counts

4 → 12

Calls

4 calls:

379.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
147.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
157.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
194.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify215.0ms

Algorithm

egg-herbie

Counts

602 → 602

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	965	8946
1	4400	7786
2	5001	7786

prune751.0ms

Filtered

602 candidates to 214 candidates (64.5%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	598	4	602
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	600	9	609

Merged error: 0b

Counts

609 → 9

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0))))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0)))))

rewrite220.0ms

Algorithm

rewrite-expression-head

Rules

834×	`*-un-lft-identity`
721×	`sqrt-prod`
514×	`associate-/r*`
436×	`sqrt-div`
398×	`frac-times`
380×	`add-sqr-sqrt`
303×	`distribute-lft-out`
245×	`add-cube-cbrt`
206×	`times-frac`
187×	`associate-r`
171×	`associate-l`
168×	`associate-/l*`
58×	`associate-/l/`
47×	`clear-num`
46×	`frac-2neg`
38×	`flip3-+` `flip-+` `unswap-sqr`
30×	`associate-*r/`
24×	`*-commutative`
23×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r/`
19×	`associate-*l/`
13×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`flip3--` `flip--`
5×	`div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `div-exp`
2×	`rem-sqrt-square` `sqrt-undiv` `hypot-udef` `prod-exp` `un-div-inv` `cbrt-unprod`
1×	`sqrt-pow1` `pow1/2` `sqrt-unprod` `pow-prod-down`

Counts

4 → 782

Calls

4 calls:

18.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
20.0ms	(/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0))))
91.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

346.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
379.0ms	(/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0))))
375.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ (hypot 1.0 0) (sqrt (* (+ (sqrt (+ x 1.0)) (sqrt x)) (- 1.0 0)))))

simplify192.0ms

Algorithm

egg-herbie

Counts

794 → 794

Iterations

Useful iterations: 1 (51.0ms)

Iter	Nodes	Cost
0	2288	15816
1	5001	15444

prune1.9s

Filtered

794 candidates to 454 candidates (42.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	792	2	794
Fresh	2	4	6
Picked	1	0	1
Done	0	2	2
Total	795	8	803

Merged error: 0b

Counts

803 → 8

regimes36.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	16	6
2	16	6

end0.0ms

sample677.0ms

Algorithm

intervals

Results

150.0ms	1679×	body	1280	valid
130.0ms	7872×	body	80	nan
90.0ms	1255×	body	640	valid
80.0ms	4148×	body	80	valid
32.0ms	625×	body	320	valid
10.0ms	293×	body	160	valid